The first-passage density, \(F_{ij}(t)\)  (\(i\ne j\) ), is defined as the probability density that a random walker starting from \(j\)  visits \(i\)  for the first
time at time \(t\) .In this paper we will only need \({\rm dS}\rightarrow {\rm dS}\)  first-passage statistics. See [1]} for \({\rm dS}\rightarrow {\rm AdS}\)  results.
The first-passage density is related to the Green's function through the well-known result [2]}:
\(\left({\rm e}^{Mt}\right)_{ij} = \int _{0^-}^t {\rm d}t^{\prime }\, \left({\rm e}^{M(t-t^{\prime })}\right)_{ii} F_{ij}(t^{\prime }) \,.\) 
